Pre-training Stage. Prior to GAN inversion, we first pre-train the textured GAN on the training split to capture desirable prior knowledge for 3D reconstruction.
As discussed in Sec. , the adversarial training of ConvMesh takes place in the UV space, where generated deformation maps and texture maps are discriminated against their corresponding pseudo ground truth.
In addition to the UV space discrimination, we further enhance the photorealism of the generated 3D objects by introducing a discriminator in the image space, following the architecture of PatchGAN as in [1]}.
The loss functions for the pre-training stage are shown as follows, where \(D_{uv}\)  and \(D_I\)  refer to the discriminators in the UV space and image space respectively, and \(\lambda _{uv}\)  and \(\lambda _{I}\)  are the corresponding weights. We use least-squares losses following [2]}. An ablation study on image space discrimination can be found in the supplementary materials.
\(\mathcal {L}_G = \lambda _{uv}_{\mathbf {z} \sim P_{\mathbf {z}}} [ (D_{uv}(G(\mathbf {z}))-1)^2 ] + \lambda _{I}_{\mathbf {z} \sim P_\mathbf {z}(\mathbf {z})} [ (D_{I}(R(G(\mathbf {z})),\mathbf {\pi })-1)^2 ].\) 
\(\mathcal {L}_{D_{uv}} = _{\mathbf {S}, \mathbf {T} \sim P_{pseudo}} [ (D_{uv}(\mathbf {S}, \mathbf {T})-1)^2 ] + _{\mathbf {z} \sim P_\mathbf {z}(\mathbf {z})} [ (D_{uv}(G(\mathbf {z})))^2 ].\) 
\(\mathcal {L}_{D_{I}} = _{\mathbf {I} \sim P_{data}} [ (D_{I}(\mathbf {I})-1)^2 ] + _{\mathbf {z} \sim P_\mathbf {z}(\mathbf {z})} [ (D_{I}(R(G(\mathbf {z})),\mathbf {\pi })^2 ].\) 
